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Ncert Solutions Maths class 11th Maths Class 11th Straight Lines

9. Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram.

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alok kumar singh | Contributor-Level 10

4 months ago

Let A (–2, –1), B (4, 0), C (3, 3) and D (–3, 2) be the given points.

Slope of DC = $\frac{3 - 2}{3 - (- 3)} = \frac{1}{3 + 3} = \frac{1}{6}$

As slope of AB = slope of DC

We conclude that AB | | DC.

Similarly, slope of BC = $\frac{3 - 0}{3 - 4} = \frac{3}{- 1} = - 3$

Slope of AD = $\frac{2 - (- 1)}{- 3 - (- 2)} = \frac{2 + 1}{- 3 + 2} = \frac{3}{- 1} = - 3$

As slope of BC = slope of AD we conclude that BC | | AD.

Hence, as the pair of opposite sides of ABCD are parallel we can conclude that the given points are the vertices of a parallelogram.

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9. Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram.

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